bio | website | math.univ-toulouse.fr/… |
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location | Toulouse | |
age | 43 | |
visits | member for | 2 years, 8 months |
seen | 2 days ago | |
stats | profile views | 1,998 |
Chercheur au CNRS, working in Toulouse.
I don't usually comment or answer questions from anonymous users.
Apr 1 |
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Are there perverse sheaves on abelian varieties with small Euler characteristic?
Isn't $d=g$ in your last statement ? |
Apr 1 |
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Is it possible to prove Mordell's conjecture geometrically?
This is a good question. It has always struck me that the only known proofs of the Mordell conjecture over number fields, as well as of the Manin-Mumford conjecture require arithmetic models. The only thing I know in the "purely complex" (or "geometrical") direction is Zannier-Pila's approach to Manin-Mumford (but not Mordell...), which still requires arithmetics, but less so than Raynaud's (or Ullmo-Szpiro-Zhang, or Pink-R.'s). |
Mar 23 |
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Chow ring of a $\mu_2$-gerbe
I have only recently come across your question. Do you actually mean a $\mu_2$-torsor ? |
Mar 23 |
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Inequality regarding sum of gaussian on lattices
It might be interesting to consider the special case where the lattice comes from the fractional ideal of a number field. Then you could use the functional equation of the theta function. See arxiv.org/pdf/math/9802121v3.pdf or math.univ-toulouse.fr/~rossler/mypage/pdf-files/… |
Mar 21 |
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A naive algebraic geometry question
See Hartshorne, Ex. III.4.2, p. 222 (Chevalley's theorem). |
Mar 12 |
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Chow ring of two varieties
This is true for varieties having an 'algebraic cellular decomposition'. See Example 19.1.11 in Fulton, Intersection Theory, p. 378. |
Mar 12 |
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Given a morphism of schemes, when does bijective + isomorphic tangent spaces = isomorphism?
See Lemma 2.4, p. 172 in Cornell-Silverman, 'Arithmetic Geometry' (article by Milne) for a statement in the direction of what you are looking for. |
Mar 11 |
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Chow ring of two varieties
About this, see Ex. IV.4.10 in Hartshorne. |
Mar 9 |
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Formal completion of the normal bundle
I think you need to complete the symmetric algebra along the augmentation ideal to get the iso. of $k$-algebras you mention. |
Mar 8 |
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Formal completion of the normal bundle
@Will Savin: PS: The OP considers the formalisation of $Z$ inside $N_{Z/X}$, not the formalisation of $N_{Z/X}$ (unless I have been completely mislead). |
Mar 8 |
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Formal completion of the normal bundle
@Will Savin: what do you mean by 'the completion is a bundle' ? |
Mar 8 |
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Formal completion of the normal bundle
PS The above is only valid in char. 0 because it uses the exponential map. |
Mar 8 |
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Formal completion of the normal bundle
Suppose for a moment that the ideal $Z$ is generated by an element, which is not a zero divisor and that $Z$ is smooth over the base field. Then Lemma 3.6 in 'Differential algebra - a scheme theory approach' by H. Gillet will prove that the answer is yes. Note that the isomorphism depends on the choice of a derivation. The general case (if $Z$ is smooth) should be provable along the same lines. For a general schematic regular immersion, I think this still works, if you can produce the relevant derivations (my guess is: if the normal bundle is trivial). |
Mar 5 |
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Log forms and Tate classes
If $X$ is proper over $\bf C$ then any such $f_i$ would be constant. But maybe you mean that the expression is local ? |
Mar 5 |
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Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
Actually, I don't know such counterexamples. The only ones I know are the classical ones (ie those mentioned at the end of the article of Deligne-Illusie). |
Mar 4 |
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Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
... But if you require the Frobenius itself to lift to $W_2(k)$, then the curve has to be ordinary. See for instance Prop. 8.6 in 'Frobenius et dégénérescence de Hodge' by L. Illusie (this is also a result of Nakkajima). |
Mar 4 |
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Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
In Berthelot-Ogus, it is supposed that the Frobenius lifts to an entire formal lifting, which is a stronger hypothesis. Nevertheless, the proof of Th. 8.8 in Berthelot-Ogus does not depend on the whole strength of this hypothesis, I think (that is why I wrote 'essentially'). As far as supersingular elliptic curves are concerned, the result of Deuring shows that the curve lifts to a CM curve and therefore a certain power of Frobenius lifts (if $k$ is a finite field). Nevertheless, the lifting will in general be defined over a ramified extension, unlike here. ... |
Mar 4 |
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Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
To put a condition on Frobenius lift is too strong. For instance, it forces ordinarity. Also I think that the result you are referring to is basically already in Th. 8.8 of the notes of Berthelot-Ogus on crystalline cohomology. |
Feb 27 |
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Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
There is something in this direction in the paper by Deligne-Illusie: see eq. (2.2.1) p. 254 in their paper in Invent. Math. 89. |
Feb 25 |
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Whether the multiplicity changes under a fields extension
What is the 'original image of $\xi$ in $X\times_k X$' ? |